Abstract
Purpose: The present study examine implied volatility spillover and transmission between emerging (India) and mature stock markets (US, France, Germany and Switzerland), measured by their respective implied volatility indices i.e. IVIX, VIX, VCAC, VDAX and VSMI. Methodology: The asymmetries in Implied Volatility (IV) indices of selected countries are examined using Engle and Ng (1993) test. The spillovers and transmission are examined in multivariate-GARCH framework using BEKK and DCC model. The analysis is done using weekly data for period spanning from Nov, 2007 to Oct, 2011March.
Findings: The main findings of study document asymmetries in the IV indices exist for the Indian, American and French markets. The BEKK-GARCH model results show that conditional variances of implied VI of India, Germany, French and Switzerland strongly affected by their own past shocks and volatility effects. The DCC model reveals that there is a moderate-level of correlation between the selected markets.
Practical Implications: The results of the present study can be used by the portfolio managers and market participant for yielding the diversification benefits in short-run by including IV indices as an asset in their portfolio.
Keywords: Implied Volatility Index, Indian Stock Market, BEKK-GARCH, DCC, VIX, VSMI
Mature Markets Implied Volatility Indices
Karam Pal Narwal*, Ved Pal Sheera**, Ruhee Mittal***
* Professor, Haryana School of Business, Guru Jambheshwar University of Science and Technology, Hisar (Haryana). Author can be contacted at email-id: karampalhsb@gmail.com (Corresponding Author)
** Professor, Haryana School of Business, Guru Jambheshwar University of Science & Technology, Hisar, Haryana *** JRF, Haryana School of Business, Guru Jambheshwar University of Science & Technology, Hisar, Haryana
1. Introduction
The study of dynamic spillovers and transmission of the large shocks between the international stock markets is becoming essential to understand the mechanism of market integration, cycles of boom and stress and analysis
of financial crisis. Majority of studies in the past have
focused on the price of an asset, thus innovations in price of volatility is becoming a promising area to explore. (Wagner
and Szimayer, 2004). The price of an option reflects market
participants’ consensus views about the expected future volatility of an underlying asset over its remaining life. The implied volatility imbedded in the option prices acts as a forward-looking measure of the expected volatility and help in the assessment of the risk over a given time
period (Mayhew, 1995). Thus, on the basis of the past
literature, it can be derived that the information content of implied volatilities is considered to be superior over ex post measures of volatilities (Fleming, Ostdiek, & Whaley,
1995; Moraux, Navettte, & Villa, 1999; Christensen & Prabbala, 1998 and Poon, & Taylor, 2001).
In 1993, Chicago Board of Options Exchange (CBOE)
launched an implied volatility index (hereafter VI), based
on the implied volatilities of OEX options. VI provides
not only short term stock volatility but also offers market volatility “standard” upon which derivatives contracts
may be written (Whaley, 1993). This index soon became
a benchmark for measuring risk in the US equity markets. A valuation model proposed by Whaley was used for
the computation of the VIX; it is called a non-model free methodology. In 2003, CBOE introduced a new methodology for the computation of VIX index using not only just at-the-money call and put option but also
out-of-money call and put options of the underlying index
S&P 500. In this case, valuation model was not necessary for the computation of VI, thus, it is called model-free methodology. Following the footsteps of CBOE, many financial markets introduced their own implied VI for instance Eurozone markets constructed VDAX, VCAC, VSMI, VEL and many more.. This index is often termed
as “investor fear gauge” as it indicates expected future stock volatility. Further, a negative contemporaneous relationship between underlying index and changes in
the volatility index has been reported in the literature
for different financial markets. Thus, market participants consider VIX as a world’s premier barometer of investor
sentiment and market volatility.
The purpose of this study is to provide new evidence on the stock market integration by examining the spillover
and transmission of the newly developed implied VI in the Asian markets i.e. Indian Volatility Index (hereafter
IVIX) on the VIX, VDAX, VCAC and VSMI. This study
is motivated by earlier stock market studies on volatility transmission using historical volatility (Koutmos and
Booth, 1995; and Cifarelli and Paladino, 2005); stock
market integration based on the realized volatility, realized returns and implied volatilities (Hamao et al,
1990; Koutmos, 1996; and Nikkinen and Sahlström, 2004); and dynamic behavior of implied volatility
transmission across the markets (Wagner and Szimayer,
2004; Skiadopoulos, 2004; Äjiö, 2008; Badshah, 2009 and Nousianinen, 2010).
Thus, the paper contributes to the existing market volatility literature by focusing on the newly developed
VI of India. In this study, the prior literature is extended in
the three important ways. Firstly, the asymmetric effects in the residual conditional variances for the international equity markets are examined. Secondly, the implied volatility spillovers and transmission effects in the India
VI vis-à-vis the international volatility indices, using the
BEKK-GARCH model are captured. Finally, the dynamic
conditional correlations and volatilities (variance equation) between the volatility indices are examined. The study is
in similar spirit with the work of Nousiainen, 2010 who
analyzed the implied volatility spillover and asymmetric
volatility effects for the four financial markets.
The paper is organized as follows. In the first section the review of literature on implied VIs and the research gap identified is given. Section two describes the research methodology including objectives, model specification
and data adopted in the study. Section three is devoted to the empirical analysis and results of the study. Finally,
Section four throws light on findings, conclusion and
policy implication of the study.
2. Review of Literature
The primary research on Volatility Indices (VI) is based on
explaining its uses, information content and characteristics.
Earlier, the implied VI was merely a theoretical idea
used in option pricing and risk management. But with
the development of derivative based products of VI, it
has become an important tool for hedging and portfolio
management. A brief review on journey of VI is divided
into two sections:
2.1 Volatility Indices Related Research
The earlyproposals which used VI as an underlying asset
for trading volatility goes back to Gastineau (1977), Galai (1979), and Brenner and Gali (1993). Whaley (1993)
showed how volatility derivative can be used by option market makers, portfolio managers and covered call writers for hedging the market volatility risk. Thus, in
1993, Chicago Board Options Exchange (CBOE) officially introduced its first implied VI, ticker symbol VIX, which
has become the benchmark for risk measurement of the
US Equity markets. Flemming et al (1995) investigated
a strong contemporaneous negative correlation between
the index returns and VIX changes. Whaley (2000) found that VIX as an indicator of expected future stock market
volatility and hence termed it as “The Investors Fear gauge”.
Moraux et al. (1999), Gazda and Výrost (2003), Skiadoploulos (2004), Duestche Borse (2005), Maghrebi et al (2007), Siriopoulos and Fassas (2008), SIX Swiss Exchange Ltd (2010) studied the volatility indices of the French , Slovakia, Greek, European, Korean, London and
Swiss stock markets respectively and examined their in-formation content and forecasting abilities.
Giot (2005) dealt with the information content of the VXO, VXN and VIX and found future stock returns are positive
and negative after high (low) levels of implied volatility
index. Carr and Wu (2006) defined the new methodology of VIX and showed that the VIX can predict movements
in the future realized variance when compared to the historic estimation of GARCH volatilities.
Fernandes et al. (2007) gave the parametric and
semi-parametric heterogeneous autoregressive (HAR)
processes for modelling and forecasting VIX. Similarly, Ahoniemi (2008) found that ARIMA (1,1,1) can be used for forecasting the direction of change in VIX correctly. Degiannakis (2008) used fractionally integrated ARIMA model for forecasting VIX. Gonazàlez and Novales (2009) and Sarwar, 2010 provide evidence for negative
and changes in the VI. A new dimension of relationship
between fear gauge index and gold price in US markets
was explored by Cohen and Qadan (2010).
2.2 Volatility Transmission and Spillovers:
Aboura (2003)
Initiated the research on international volatility transmission by using VIs (VX1, VDAX and VIX). The interactions between implied volatility of different markets were captured using the multivariate-GARCH
framework and mean-reverting jump diffusion model.
Wagner and Szimayer (2004) investigated the transmission of shocks for the US and German implied volatility indices using mean reversion model that allows for the Poisson
jumps. Äjiö, (2007) present the stock market integration
by examining the implied volatility term structures
between the VDAX, VSMI and VSTOXX volatility
indices. The correlation structures indicated that they are
closely related to each other. In 2009, Badshah examined the dynamic implied volatility transmission across the VIs (VIX, VXN, VDAX and VSTOXX) using the Granger
Causality, generalized impulse response functions and the variance decomposition method.
2.3 Research Gap
The insight to the past literature lays the foundation for
present study. The India VIX being a newly developed
index in the Asian markets, not much attention is given to this index. Till now studies have focused on the implied
VI of the American and European countries. To the best of the knowledge no significant work is done to examine
the volatility spillovers and transmission effects between the implied volatility indices of Indian stock markets and international equity markets.
3. RESEARCH METHODOLOGY
3.1 Objectives of the Study
The objective of the study is to examine the implied
volatility spillover and transmission for the emerging (India) and the mature stock markets (US, France, Germany and Switzerland) as measured by their respective implied
volatility indices i.e. IVIX, VIX, VCAC, VDAX and VSMI. In the present study, the volatility spillovers and
transmission effects in the Indian markets are examined with respect to the US, France, Germany and Swiss markets.
The following hypotheses are formulated for the purpose of research:
Hypothesis I: Asymmetries exist in the volatility indices.
Hypothesis II: There are implied volatility and shock spillovers between Indian and the selected international markets volatility indices.
Hypothesis III: To account for the possibilities that volatilities and the correlation are dynamically changing over the time, for the Indian markets w.r.t. to international markets.
3.2 Model Specifications
3.2.1. Asymmetries in Volatility
The Engle and Ng (1993) sign and size bias test is applied
to assess the asymmetric response of the variance to the past information. This test is based on studying the error
terms generated from the standard GARCH (1,1) model:
where
(i)
(ii) where, is mean, y is return series at time t, is the squared conditional volatility at time t, and is the lagged and the square error terms of the mean equation,
which are normally distributed with zero mean. The α and β are the non-negative coefficients, with α+β < 1 condition. Then the Engle-Ng-test is applied on the error
terms is:
and TR2 (3) (iii)
Where, are the before mentioned error terms, are
the coefficients, and are the dummies
for the negative and positive error terms and is the
existence of sign bias, which signifies that the return
volatility is larger in the bearish phase as compared to
the bullish period. Whereas, significant
reveals the (negative) positive size bias which means that magnitude of shocks have differing impacts.
3.2.2. BEKK-GARCH Model
To investigate the volatility spillovers, the BEKK (Baba, Engle, Kraft and Kroner) representation of multivariate GARCH (p,q) proposed by Engle and Kroner (1995) is applied. The BEKK (1, 1) representation is of the
following form:
(iv) Where, is the k×k lower triangular matrix and
are the parameter matrices. The diagonal elements in matrices A and G measures the effect of the lagged volatility on its conditional volatility. The off-diagonal elements in matrices A(aij) and G(gij) capture the cross-market effects of shocks and volatility spillovers.
3.2.3. Dynamic Conditional Correlation Models
Bollerslev (1990) introduced a class of multivariate
GARCH model based on the assumption of constant conditional correlations (CCC). A generalization of CCC
model was proposed by Engle and Sheppard (2001); Engle
(2002) and Tse amd Tsui (2002) in which the conditional correlation matrix is time dependent. This model is known
as Dynamic conditional correlation (DCC).
The DCC model of Engle (2002) computes the
time-variant conditional correlation matrix can be expressed as:
(v)
(vi) Where, , is a k×k symmetric positive unconditional variance matrix, is k×k diagonal matrix with time-varying standard estimated by univariate GARCH model applied to individual time series and is the
standardized residuals defined as
and are the non-negative scalar
parameters satisfying the condition < 1. Whereas, Tse and Tsui (2002) proposed a slightly different formulation:
Table 1: Market Data
Volatility Index Name Underlying Stock index
Market Market Description
IVIX (Indian Volatility Index) S&P CNX
Nifty India Largest emerging market and among world largest stock exchange in terms of market capitalization based on 50 major
-stocks
CBOE Volatility Index, or VIX S&P 500 USA Largest US option exchange, first organized market to began trading in options
CAC 40 Volatility Index, or VCAC CAC 40 France (Paris) One of the main national indices of the pan-European stock
exchange group Euronext, index represents capitalization weighted measure of 40 most significant stock among top 100 active stocks.
VDAX-NEW Volatility Index DAX Germany
(Frankfurt)
30 major German companies trading on the Frankfurt Stock Exchange, main European continental market
VSMI Volatility Index SMI Switzerland Developed country market away from the hubs, the underly
-ing index comprises 50 largest and most liquid stocks in the
Swiss equity market.
(vii) Where, is the time-invariant positive definitive
parametric matrix with unit diagonal element and is k×k is sample correlation matrix of the past standardized residuals. The log-likelihood estimator can be written as:
(viii)
3.3 DATA
3.3.1 Data Collected
The daily closing values of implied VI running from 1 Nov, 2007 to 30 Oct, 2011 for the countries mentioned in
Table I is used for the purpose of research. The problem of non-synchronies in the daily data is mitigated by converting it into weekly data. The average of the daily data of each week is taken to synchronise the series of different countries. The data is extracted from the respective authentic websites of various market indices.
3.3.2 Properties of Data
The innovations (changes) in the weekly data of the volatility indices are calculated by:
(ix)
Descriptive Statistics: The descriptive statistics for the
changes in weekly univariate VI series are presented in the Table 2. The mean values for the changes in the VIs
are positive and small. All distributions are positively
skewed where the IVIX and VSMI have the lowest and highest values respectively and leptokurtic where VCAC and VDAX have the lowest and highest values. The results
of Jarque-Bera statistics indicates that the series are
non-normally distributed. The joint Ljung-Box Q-statistics with
different lags reveals weak evidence of autocorrelations
and heteroscedasitictiy for IVIX at 8 and 12 lags whereas for the VIX and VSMI is shown at 12 lag. The ARCH LM
test for the autocorrelations in the standardized residuals
reveals ARCH effects exist for VDAX, VCAC and VSMI at 1% significance level for different lags. There is weak evidence for the presence of ARCH-effects in the VIX
and no ARCH-effect or heteroscedasticities is determined
in the Indian VI, the latter finding of which is surprising.
Table 2: Descriptive Statistics of innovations in VI
IVIX VIX VDAX VCAC VSMI
Mean -0.00217 0.001242 0.002399 0.001963 0.000606 Median -0.00525 -0.01351 -0.00388 -0.00742 -0.01087 Maximum 0.39918 0.396445 0.475686 0.37877 0.472906 Minimum -0.31818 -0.27027 -0.29489 -0.27281 -0.2998 Std. Dev. 0.096773 0.103397 0.106315 0.106725 0.10773 Skewness 0.429527 0.681813 0.784823 0.552204 0.713827 Kurtosis 5.30508 4.466709 5.463107 4.403862 5.218151 Jarque-Bera 52.69733* 34.9266* 74.28802* 27.78431* 60.59594* Observations 209 209 209 209 209 LB(4) 1.4626 3.5602 0.8234 0.5318 1.4461 LB(8) 15.559**` 10.02 6.4899 9.5719 8.6287 LB(12) 19.938*** 20.733*** 14.029 15.165 19.293*** ARCH(4) 1.2367 9.7631** 30.3942* 21.4485* 29.6757* ARCH(8) 3.5611 12.9542 31.9435* 23.9195* 32.9887* ARCH(12) 4.8795 15.1142 39.8819* 28.3171* 36.2180*
Figure 1: Logarithms of Volatility Indices 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 2008 2009 2010 2011 LIVIX 2.4 2.8 3.2 3.6 4.0 4.4 2008 2009 2010 2011 LVIX 2.4 2.8 3.2 3.6 4.0 4.4 2008 2009 2010 2011 LVDAX 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 2008 2009 2010 2011 LVCAC 2.4 2.8 3.2 3.6 4.0 4.4 2008 2009 2010 2011 LVSMI Source: Authors
Figure 2: Graph showing Changes/Innovations in Volatility Indices -.4 -.3 -.2 -.1 .0 .1 .2 .3 .4 .5 2008 2009 2010 2011 IVIX -.3 -.2 -.1 .0 .1 .2 .3 .4 .5 2008 2009 2010 2011 VIX -.4 -.3 -.2 -.1 .0 .1 .2 .3 .4 .5 2008 2009 2010 2011 VDAX -.3 -.2 -.1 .0 .1 .2 .3 .4 2008 2009 2010 2011 VCAC -.4 -.3 -.2 -.1 .0 .1 .2 .3 .4 .5 2008 2009 2010 2011 VSMI Source: Authors
3.3.3 Unconditional Correlations
The unconditional correlations (Table 3) of the change in
VIs show that the American and European markets are
highly correlated whereas Indian markets have shown low level of correlation with the other four markets. The
main European markets i.e. German-French markets (0.895) and German- Swiss markets (0.926) are the most
correlated. The Indian market has shown least correlation
with the American market (0.408) and with European markets also the range of correlation is 0.421-0.488.
Table 3: Unconditional Correlations of change in Volatility Indices
IVIX VIX VDAX VCAC VSMI
IVIX 1 VIX 0.408* 1 VDAX 0.488* 0.845* 1 VCAC 0.421* 0.823* 0.895* 1 VSMI 0.479* 0.832* 0.926* 0.878* 1 Source: Authors
Note: *=1% level of significance
Thezse properties of volatility indices can be also seen
graphically. As the Figure 1 show that the overall counters
of the logarithms-level VIs are almost identical, showing
similar patterns during the bullish and bearish phase, as in the beginning and end of time series. The Figure 2 shows
the innovations/ changes in the VIs.
3.3.4 Unit Root Tests
The unit root tests are applied to examine the potential diversions of the time series data from the stability. The
standard Augmented Dickey-Fuller (ADF) (Dickey and Fuller, 1981) in addition with the Phillips-Perron (Phillips and Perron, 1988) and KPSS (Kwiatkowski et al., 1992) test are applied to change in implied volatility indices examine stationarity (unit root) of the data series. Table 4, represents the results of three unit root test. The results for
the ADF and PP-test denote that all first difference data series are stationary at 1% level of significance. Further, the KPSS test confirms that data series are stationary at first difference, as the null hypothesis for stationary series
is accepted for all data series.
3.3.5 Asymmetries in the data
The potential asymmetries in volatilities are detected
using Engle-Ng (1993) sign and size bias test (Table 5). There are existent traces of joint asymmetry in implied
Table 4: Unit root test statistics of changes in implied VIs
Test/ Series ADF PP KPSS
1 2 3 1 2 3 1 2 IVIX -7.750(5)* -7.721(5)* -7.767(5)* -13.365(2)* -13.332(2)* -13.392(2)* 0.033(1) 0.032(1) VIX -9.159(1)* -9.140(1)* -9.182(1)* -13.805(2)* -13.773(2)* -13.837(2)* 0.057(2) 0.057(2) VDAX -9.480(1)* -9.457(1)* -9.499(1)* -13.986(1)* -13.952(1)* -14.015(1)* 0.062(1) 0.062(1) VCAC -10.425(1)* -10.401(1)* -10.449(1)* -14.066(2)* -14.032(2)* -14.099(2)* 0.048(2) 0.048(2) VSMI -9.559(1)* -9.535(1)* -9.583(1)* -13.527(3)* -13.495(3)* -13.560(3)* 0.056(3) 0.051(4)
Asymptotic critical values
1% level -3.463 -4.004 -2.576 -3.462 -4.003 -2.576 0.739 0.216
5% level -2.876 -3.432 -1.942 -2.875 -3.432 -1.942 0.463 0.146
10% level -2.574 -3.140 -1.616 -2.574 -3.139 -1.616 0.347 0.119
Source: Authors
Note: ADF is the Augmented Dickey-Fuller, PP is the Phillips-Perron, and KPSS is Kwiatkowski, Phillips, Schmidt, and Shin test.
Model Specification: 1.Intercept, 2. Intercept+trend, 3.None. The Null hypothesis for ADF and PP test: H0 = Variable is
non-stationary and for KPSS: H0 = Variable is stationary.
*, ** and *** indicate the rejection of the null hypothesis at the 1%, 5% and 10% significance levels, respectively. The proper lag
order for ADF test is chosen by considering Akaike Information Criteria, representing in parenthesis.
For KPSS and PP tests, the bandwidth is chosen using Newey–West method and spectral estimation uses Bartlett kernel, representing in parenthesis.
volatility indices of the India (12.93, significant at 1% level), America (7.36, significant at 10% level) and French (7.87, significant at 5% level) volatility indices, therefore,
accepting the null Hypothesis I for these markets. The
coefficient of S-t-1 is significant for the American, German
and Swiss markets, implying that, negative magnitude effect exist in these markets. This means that past events is
of importance and confirmed by the preliminary findings of Carr and Wu (2006). The asymmetries in the volatilities
of implied volatility indices could be the consequence of the leverage effect of the underlying stock indices.
4. EMPIRICAL RESULTS AND ANALYSIS
4.1 Spillover Effect Analysis
Table 6 summarizes the estimation results of bivariate-BEKK GARCH for the Indian markets with American and European markets in a pair wise manner. The matrices A
and G reported in the equation (iv) are useful in examining the relationship in terms of volatility. The diagonal
elements of the matrices A and G capture the ARCH and GARCH (also termed volatility persistence) effects. In
the Table 6, out of 8 estimated diagonal parameters a11 and
a22 in the each pair, 7 are statistically significant at 1% and 5% level except of a22 in the IVIX/VIX group implying
the presence of strong ARCH effects in the stock markets of India, Switzerland, Germany and France. Whereas, the diagonal elements g11 is significant in 3 cases out
of 4 suggesting the presence of GARCH effects in the Indian markets when analyzed with American, Swiss and French markets. The other diagonal parameter g22 is statistically significant for the stock markets of Germany,
France and Switzerland, thus indicating that GARCH
(1,1) process is driving the conditional variances of the
three stock markets. This implies that the conditional variances of India, Germany, French and Switzerland in the implied volatility series are strongly affected by their
own past shocks and volatility effects. Thus, implied VI is
dependent on its own volatility in the past.
Table 5: Engle-Ng (1993) Sign and Size Bias test
Variable IVIX VIX VDAX VCAC VSMI
C 1.13* (0.34) 1.25* (0.31) 0.81* (-0.26) 1.27* (0.25) 0.80* (0.25) S-t-1 -0.49 (0.35) -0.25 (0.37) 0.41 (0.37) -0.59** (0.32) 0.41 (0.41) S-t-1 ut-1 0.07 (0.09) 0.38** (0.18) 0.48* (0.27) 0.03 (0.28) 0.49*** (0.29) S+t-1 ut-1 0.46 (0.33) 0.03 (0.30) 0.36 (0.28) 0.05 (0.21) 0.36 (0.27)
Joint - x2x2 12.93* 7.36*** 6.04 7.87** 5.98
Note: Standard errors are presented in the parentheses and the levels of significance with asterisks (* = 1%, ** = 5% and *** =
10%). Estimated method is OLS with Newey-West correction for heteroscedasticity and autocorrelation. The joint test follows chi-square distribution with critical values (***1% = 11.345, **5% = 7.815 and *10% = 6.251)
Table 6: Parameter estimates for the BEKK-GARCH (1,1) Model
IVIX/VIX IVIX/VSMI IVIX/VDAX IVIX/VCAC
c11 5.311* (5.950) 6.395* (6.433) 7.393* (10.250) 6.349* (7.017) c21 -2.546 (-1.072) -1.351 (-0.636) 0.112 (0.085) -1.373 (-1.165) c22 5.988* (2.578) 2.878 (0.824) 3.468* (2.975) 0.000 (0.000) a11 0.502* (5.733) 0.328** (2.045) 0.351** (2.119) 0.530* (4.183) a12 0.237** (2.552) -0.286** (-2.321) -0.129 (-0.985) -0.249*** (-1.914) a21 -0.143 (-1.109) 0.232* (3.005) 0.216* (2.618) 0.130** (2.105) a22 0.321 (1.513) 0.586* (6.471) 0.470* (7.037) 0.485* (5.571) g11 0.619* (2.618) 0.519** (2.266) 0.263 (1.009) 0.253** (2.068) g12 0.550* (1.976) 0.458*** (1.931) 0.197 (0.626) 0.741* (18.645) g21 0.208 (0.613) 0.118 (0.759) 0.236 (1.418) 0.365* (14.565) g22 0.025 (0.070) 0.517* (4.067) 0.742* (4.601) 0.342* (10.232) Log-Likelihood -1521.250 -1513.564 -1514.424 -1523.245
The off-diagonal elements of matrices A and G capture the cross-market effects such as shock and volatility
spillover among the five stock markets. Firstly, according to the statistics in the Table 6, evidence of bidirectional shock transmission exists in IVIX/VSMI and IVIX/ VCAC, as the pairs of off-diagonal parameters a12 and
a21 are statistically significant in these stock markets.
The two-way shock spillover is an indication of strong connection between the implied volatility indices of Indian-French markets and Indian-Swiss markets. The bidirectional cross-markets shock spillover indicates that shock related news in one stock exchange effects the volatility in the other stock market and vice-versa. There
are traces of unidirectional shock spillover from IVIX to VIX and VDAX to IVIX as their respective a12 and a21 are significant (their counterparts are insignificant) in BEKK-GARCH Model for IVIX/VIX and IVIX/VDAX.
Secondly, the evidence of bidirectional volatility linkages is found only between the Indian and French markets as their g coefficients are statistically significant at 1 level. These bidirectional volatility linkages imply that a strong connection between them, as the conditional variance of
one implied VI depends on the past volatility of the IV
index of other country. In the meanwhile, there exists
unidirectional volatility spillover from IVIX to VIX and IVIX to VSMI. Thus, the null hypothesis II that there exist
implied volatility and shock spillovers between the Indian and international markets are accepted, when the ARCH (a11, a12, a22, and a21) and GARCH (g11, g12, g21 and g22)
parameters are significant.
4.2 Dynamic Conditional Correlations
The dynamic conditional correlations (DCC) table 7 and figure 3 are moderate and stable. The mean DCC is smallest between the IVIX-VIX and largest between the IVIX-VDAX. The mean and median of the DCC are
coinciding for each group of countries and the standard
deviations is also small. The DCC for the Indian markets
versus global markets varies widely. The range between
different volatility indices are: IVIX-VIX (0.05-0.703), IVIX-VDAX (-0.01913 to 0.75), IVIX-VCAC (-0.063 to 0.752) and from IVIX-VSMI (-0.036 to .740). These
graphs show the possible existence of variations and structural breaks in the dynamic correlations. Thus, the null hypothesis III is accepted, the dynamic correlations
between India and global markets are significantly
changing over the time period, and exhibit high and low level of correlations at different time periods in the various markets.
The time-varying correlations during the period of study
are positive for majority of the time, thus, indicating that
Indian markets move in tandem with the American and
the European markets. Further, most of the correlations
have the tendency to fall more, than to grow, in the face of sub-prime crisis, which started with the American
risk-based mortgage crisis in 2007. The European sovereign debt crisis in the start of 2010 and recent downgrade in the credit rating of US economy are the major events
which affected the market’s volatility across the world. Thus, a high level of conditional correlations (ranging
between 0.70-0.75 in the period post 2010) for the implied
volatility indices of Indian markets versus the American, German, French and Swiss market is observed.
Table 7: Descriptive Statistics of the Dynamic Conditional Correlations
CORRELATIONS
IVIX-VIX IVIX-VDAX IVIX-VCAC IVIX-VSMI
Mean 0.384 0.458 0.404 0.450 Median 0.391 0.462 0.407 0.478 Maximum 0.703 0.750 0.752 0.740 Minimum 0.051 -0.019 -0.063 -0.036 Std. Dev. 0.131 0.154 0.167 0.162 Skewness -0.095 -0.690 -0.354 -0.744 Kurtosis 2.865 3.588 2.927 3.326 Jarque-Bera 0.469 19.587 4.402 20.204 Probability 0.791 0.000 0.111 0.000 Observations 209 209 209 209
5. FINDINGS, CONCLUSIONS AND POLICY
IMPLICATIONS
The study investigated the nature of financial integration
among the emerging (Indian) and mature economies (America, Germany, France and Swiss markets) in using the implied volatility indices. The results describe the wider international systematic behaviour of the underlying
Asian-Pacific and Western stock markets. The results obtained from the bivariate BEKK-GARCH model are
surprising as volatility spillovers are outwards from the emerging to developed markets. But in the real world, the
mature markets are the dominant players and the financial
events happening in these markets affects the developing
Figure 3: Dynamic Conditional Correlations for the Implied Volatility Indices .0 .1 .2 .3 .4 .5 .6 .7 .8 2008 2009 2010 2011
Correlation of IVIX with VIX
-.1 .0 .1 .2 .3 .4 .5 .6 .7 .8 2008 2009 2010 2011
Correlation of IVIX with VDAX
-.1 .0 .1 .2 .3 .4 .5 .6 .7 .8 2008 2009 2010 2011
Correlation of IVIX with VCAC
-.1 .0 .1 .2 .3 .4 .5 .6 .7 .8 2008 2009 2010 2011
Correlation of IVIX with VSMI
complex phenomenon is observed as a consequence of
increased level of financial globalization.
The results of DCC-model shows that there is moderate
level of correlation in the volatility indices of the international markets with Indian markets and carry a
unified message of uncertainty in respective markets in
the long run. These results also imply that theoretically
there is possibility that of yielding diversification benefits
in short-run by making investment in the volatility indices of Indian stock markets in combination with westerns markets.
In the light of the above findings, in short-run VIs of
respective countries can be used for the international
portfolio diversification, for cash protection and hedging through local market index would bring greatest efficiency.
The fast changes in the volatility indices with respect to
the underlying indices provide an efficient picture of the
information dissemination in the markets. These facts
support important properties of VI being used as a market
indicator and market timing tool. Finally, the information transmission and spillovers are running unidirectional from Indian markets to US markets and German markets to Indian markets and bidirectional between the Indian and French markets.
5.1. Policy Implications and Future Research
The results of the present study can be used by the portfolio managers and market participant for yielding
the diversification benefits in short-run including implied
volatility indices as an asset in portfolio. The investors could also hedge their portfolios against volatility with an
This also indicates that same methodology can be applied to the volatility indices of the other countries
in the Asian and Western world, Euro currency areas
in order to compare their results with this one. It would be interesting to conduct similar study on the volatility derivative products. Finally, it would be worth studying the impact of the leverage effect in the underlying index
on the volatilities of the VI.
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